Solve {left(frac{1/2-frac{2/3right)}^2}{5/6}div5/6-sqrt{frac{1}{9}}}{sqrt[3]{frac{1}{8}}+{left(1-frac{1}{2}right)}^2frac{9}{8}}

$$\frac{ \frac{ { \left( \frac{ 1 }{ 2 } - \frac{ 2 }{ 3 } \right) }^{ 2 } }{ \frac{ 5 }{ 6 } } \div \frac{ 5 }{ 6 } - \sqrt{ \frac{ 1 }{ 9 } } }{ \sqrt[ 3 ]{ \frac{ 1 }{ 8 } } + { \left(1- \frac{ 1 }{ 2 } \right) }^{ 2 } \frac{ 9 }{ 8 } }$$

Evaluate

$$-\frac{704}{1875}\approx -0.375466667$$

Solution Steps

Divide \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} by \frac{5}{6} by multiplying \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} by the reciprocal of \frac{5}{6}.

$$\frac{\frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}\times 6}{\frac{5}{6}\times 5}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Subtract \frac{2}{3} from \frac{1}{2} to get -\frac{1}{6}.

$$\frac{\frac{\left(-\frac{1}{6}\right)^{2}\times 6}{\frac{5}{6}\times 5}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Calculate -\frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{\frac{\frac{1}{36}\times 6}{\frac{5}{6}\times 5}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Multiply \frac{1}{36} and 6 to get \frac{1}{6}.

$$\frac{\frac{\frac{1}{6}}{\frac{5}{6}\times 5}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Multiply \frac{5}{6} and 5 to get \frac{25}{6}.

$$\frac{\frac{\frac{1}{6}}{\frac{25}{6}}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Divide \frac{1}{6} by \frac{25}{6} by multiplying \frac{1}{6} by the reciprocal of \frac{25}{6}.

$$\frac{\frac{1}{6}\times \frac{6}{25}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Multiply \frac{1}{6} and \frac{6}{25} to get \frac{1}{25}.

$$\frac{\frac{1}{25}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1}{25}-\frac{1}{3}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Subtract \frac{1}{3} from \frac{1}{25} to get -\frac{22}{75}.

$$\frac{-\frac{22}{75}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Calculate \sqrt[3]{\frac{1}{8}} and get \frac{1}{2}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\left(\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\frac{1}{4}\times \frac{9}{8}}$$

Multiply \frac{1}{4} and \frac{9}{8} to get \frac{9}{32}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\frac{9}{32}}$$

Add \frac{1}{2} and \frac{9}{32} to get \frac{25}{32}.

$$\frac{-\frac{22}{75}}{\frac{25}{32}}$$

Divide -\frac{22}{75} by \frac{25}{32} by multiplying -\frac{22}{75} by the reciprocal of \frac{25}{32}.

$$-\frac{22}{75}\times \frac{32}{25}$$

Multiply -\frac{22}{75} and \frac{32}{25} to get -\frac{704}{1875}.

$$-\frac{704}{1875}$$

Factor

$$-\frac{704}{1875} = -0.37546666666666667$$